To avoid the collapse of multiple subspaces into a single point, we insert a contrastive term [1]} to balance the loss, which encourages the projected points in \(\mathcal {S}_i\)  to move away from each other.
The resulting distance loss is therefore written as:
\(\mathcal {L}_{dis}=\hspace{-0.85355pt} \sum _{i=1}^{k} \hspace{-0.85355pt} (1\hspace{-1.70709pt}-\hspace{-1.70709pt}\alpha _i) \delta _{i}^2+ \alpha _i\hspace{-1.70709pt}\max (m\hspace{-1.70709pt}-\hspace{-1.70709pt} \delta _{i},\hspace{-1.42271pt}0)^2\) 
